Maximum-likelihood time-of-arrival estimation for saturated optical transient signals

Area of Science:

• Optical signal processing
• Statistical modeling
• Time-series analysis

Background:

• Transient optical signals are crucial in various scientific fields.
• Estimating signal arrival times is often complicated by saturation distortion.
• Existing methods may not adequately handle censored data.

Purpose of the Study:

• To develop robust maximum-likelihood procedures for estimating transient optical signal arrival times.
• To address signal distortion caused by saturation effects.
• To evaluate the performance of these new procedures compared to existing algorithms.

Main Methods:

• Employing right-censored Poisson point process models.
• Modeling Poisson intensity with a template, unknown scaling factor, and additive background counts.
• Utilizing Monte Carlo simulations to assess algorithm performance.

Main Results:

• The proposed maximum-likelihood procedures effectively estimate arrival times of transient optical signals.
• Performance is characterized as a function of signal magnitude and saturation threshold.
• Significant benefits are observed over algorithms that do not account for censoring.

Conclusions:

• Right-censored Poisson point process models provide a powerful framework for analyzing saturated transient optical signals.
• The developed maximum-likelihood procedures offer improved accuracy in arrival time estimation.
• Accounting for signal censoring is critical for reliable analysis.